### Linear Algebra (MATH-203)

Course Outline (Fall Semester 2020)

• Course Title: Linear Algebra
• Course Code: MATH-203
• Credit Hours: 03
• Instructor: Memoona Nawaz
• Email: [email protected]

Introduction to Course:

Linear algebra is the study of linear systems of equations, vector spaces, and linear transformations. Solving systems of linear equations is a basic tool of many mathematical procedures used for solving problems in science and engineering.

Learning Outcomes:

At the end of this course the student will be able to:

• Solve linear systems of equations,
• Comprehend vector spaces, subspaces and inner product spaces,
• Understand fundamental properties of matrices including determinants, inverse matrices, matrix factorizations, eigenvalues, orthogonality and diagonalization,
• Have an insight into the applicability of linear algebra,
• Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra.

Course Contents:

1. Introduction to Vectors: Vectors and Linear Combinations, Lengths and Dot Products, Matrices.
2. Solving Linear Equations: Vectors and Linear Equations, the Idea of Elimination, Elimination Using Matrices, Rules for Matrix Operations, Inverse Matrices.
3. Elimination = Factorization; A = LU, Transposes and Permutations.
4.  Vector Spaces and Subspaces: Spaces of Vectors, The Null space of A: Solving Ax = 0, The Rank and the Row Reduced Form, the Complete Solution to Ax = B, Independence, Basis and Dimension, Dimensions of the Four Subspaces.
5. Orthogonally: Orthogonally of the Four Subspaces, Projections, Least Squares Approximations, Orthogonal Bases and Gram-Schmidt.
6. Determinants: The Properties of Determinants, Permutations and Cofactors, Cramer's Rule, Inverses, and Volumes.
7. Eigenvalues and Eigenvectors: Introduction to Eigenvalues, Diagonalizing a Matrix, Applications to Differential Equations, Symmetric Matrices, Positive Definite Matrices, Similar Matrices, Singular Value Decomposition (SVD).
8. Applications: Matrices in Engineering, Graphs and Networks, Markov Matrices, Population, and Economics; Linear Programming, Fourier series: Linear Algebra for Functions, Linear Algebra for Statistics and Probability, Computer Graphics.
9. Numerical Linear Algebra: Gaussian Elimination in Practice, Norms and Condition Numbers, Iterative Methods for Linear Algebra.
10. Complex Vectors and Matrices: Complex Numbers, Hermitian and Unitary Matrices, Matrix Factorizations.

Textbook(s):

Introduction to Linear Algebra by Gilbert Strang, Wellesley Cambridge Press; 4th Edition (February 10, 2009).

Reference Material:

1.  Elementary Linear Algebra with Applications by Bernard Kolman, David Hill, 9th Edition, Prentice Hall PTR, 2007.
2.  Linear Algebra And Its Applications by Gilbert Strang, Strang, Brett Coonley, Andrew Bulman-Fleming, 4th Edition, 2005.
3. Elementary Linear Algebra: Applications Version by Howard Anton, Chris Rorres, 9th Edition, Wiley, 2005.
4. Linear Algebra and Its Applications by David C. Lay, 2nd Edition, Addison-Wesley, 2000.
5. Linear Algebra by Harold M. Edwards, Birkhäuser; 1st Edition, 2004.
6. Linear Algebra: A Modern Introduction by David Poole by Brooks Cole, 3rd Edition.

Suggested Books:

• Linear Algebra by David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron.
•  Linear Algebra and Its Applications by David C Lay and Steven R Lay.
• Schaum’s Outline of Theory and Problem of Linear Algebra. Seymour Lipschutz. Mc-Graw Hill.

ASSESSMENT CRITERIA:

Total Marks: 100

Mid-Term Exam:  30

Final-Term Exam: 50

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Key Dates and Time of Class Meeting:

Program: BSIT(2019-2023)

Class: Self-Support (3rd-Semester)

Wednesday:                                                              11:00 AM - 12:30 PM

Thursday:                                                                 11:00 AM - 12:30 PM